Operation
The Gresley conjugated gear is effectively an adding machine, where the position of the valve for the inside cylinder is the sum of the positions of the two outside cylinders, but reversed in direction. It can also be thought of as a rocking lever between one outside cylinder and the inside cylinder, as is common on 4-cylinder steam locomotives, but with the pivot point being moved back and forth by a lever from the other outside cylinder.
If we approximate the motion of each valve by a sine wave — if we say the position of a valve in its back-and-forth travel is exactly proportional to the sine of the "driver angle", once we have set the zero point of driver angle at the position it needs to be for that valve — then the mathematics is simple. The position of the valve that is pinned to the long end of the 2-to-1 lever is, while the positions of the other two valves are supposed to be and . The position of the short end of the 2-to-1 lever is —which, it turns out, is midway between and for any value of . So a 1-to-1 lever pivoted on the short arm of the 2-to-1 lever will do the trick.
Read more about this topic: Gresley Conjugated Valve Gear
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—Francis Bacon (1560–1626)
“An absolute can only be given in an intuition, while all the rest has to do with analysis. We call intuition here the sympathy by which one is transported into the interior of an object in order to coincide with what there is unique and consequently inexpressible in it. Analysis, on the contrary, is the operation which reduces the object to elements already known.”
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“You may read any quantity of books, and you may almost as ignorant as you were at starting, if you don’t have, at the back of your minds, the change for words in definite images which can only be acquired through the operation of your observing faculties on the phenomena of nature.”
—Thomas Henry Huxley (1825–95)